Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/3170
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dc.contributor.authorDu, Yihongen
dc.contributor.authorGuo, Yuxiaen
dc.date.accessioned2009-11-19T16:15:00Z
dc.date.issued2003en
dc.identifier.citationTopological Methods in Nonlinear Analysis, 22(1), p. 69-92en
dc.identifier.issn1230-3429en
dc.identifier.urihttps://hdl.handle.net/1959.11/3170en
dc.description.abstractWe consider the elliptic problem -Δu - λu = a(x)g(u), with a(x) sign-changing and g(u) behaving like u^p, p > 1. Under suitable conditions on g(u) and a(x), we extend the multiplicity, existence and nonexistence results known to hold for this equation on a bounded domain (with standard homogeneous boundary conditions) to the case that the bounded domain is replaced by the entire space ℝ^N. More precisely, we show that there exists Λ > 0 such that this equation on ℝ^N has no positive solution for λ > Λ, at least two positive solutions for λ ∈ (o,Λ), and at least one positive solution for λ ∈ (-∞,0]U{A}. Our approach is based on some descriptions of mountain pass solutions of semilinear elliptic problems on bounded domains obtained by a special version of the mountain pass theorem. These results are of independent interests.en
dc.languageenen
dc.publisherJuliusz Schauder Centeren
dc.relation.ispartofTopological Methods in Nonlinear Analysisen
dc.titleMountain Pass Solutions and an Indefinite Superlinear Elliptic Problem on ℝ^Nen
dc.typeJournal Articleen
dc.subject.keywordsOrdinary Differential Equations, Difference Equations and Dynamical Systemsen
local.contributor.firstnameYihongen
local.contributor.firstnameYuxiaen
local.subject.for2008010109 Ordinary Differential Equations, Difference Equations and Dynamical Systemsen
local.subject.seo2008970101 Expanding Knowledge in the Mathematical Sciencesen
local.profile.schoolSchool of Science and Technologyen
local.profile.emailydu@une.edu.auen
local.output.categoryC1en
local.record.placeauen
local.record.institutionUniversity of New Englanden
local.identifier.epublicationsrecordpes:733en
local.publisher.placeTorun, Polanden
local.format.startpage69en
local.format.endpage92en
local.peerreviewedYesen
local.identifier.volume22en
local.identifier.issue1en
local.contributor.lastnameDuen
local.contributor.lastnameGuoen
dc.identifier.staffune-id:yduen
local.profile.roleauthoren
local.profile.roleauthoren
local.identifier.unepublicationidune:3255en
dc.identifier.academiclevelAcademicen
local.title.maintitleMountain Pass Solutions and an Indefinite Superlinear Elliptic Problem on ℝ^Nen
local.output.categorydescriptionC1 Refereed Article in a Scholarly Journalen
local.relation.urlhttp://www.tmna.ncu.pl/files/v22n1-04.pdfen
local.description.statisticsepubsVisitors: 224<br />Views: 225<br />Downloads: 0en
local.search.authorDu, Yihongen
local.search.authorGuo, Yuxiaen
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School of Science and Technology
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